A309486 Sum of the squarefree parts of the partitions of n into 10 parts.

0, 0, 0, 0, 0, 0, 0, 0, 0, 0, 10, 11, 24, 35, 66, 97, 160, 223, 343, 485, 714, 952, 1357, 1808, 2469, 3237, 4329, 5576, 7335, 9322, 12028, 15148, 19232, 23934, 30025, 37070, 45915, 56180, 68950, 83661, 101771, 122540, 147797, 176821, 211682, 251515, 299136

Offset

0,11

Links

David A. Corneth, Table of n, a(n) for n = 0..9999

Index entries for sequences related to partitions

Formula

a(n) = Sum_{r=1..floor(n/10)} Sum_{q=r..floor((n-r)/9)} Sum_{p=q..floor((n-q-r)/8)} Sum_{o=p..floor((n-p-q-r)/7)} Sum_{m=o..floor((n-o-p-q-r)/6)} Sum_{l=m..floor((n-m-o-p-q-r)/5)} Sum_{k=l..floor((n-l-m-o-p-q-r)/4)} Sum_{j=k..floor((n-k-l-m-o-p-q-r)/3)} Sum_{i=j..floor((n-j-k-l-m-o-p-q-r)/2)} (r * mu(r)^2 + q * mu(q)^2 + p * mu(p)^2 + o * mu(o)^2 + m * mu(m)^2 + l * mu(l)^2 + k * mu(k)^2 + j * mu(j)^2 + i * mu(i)^2 + (n-i-j-k-l-m-o-p-q-r) * mu(n-i-j-k-l-m-o-p-q-r)^2), where mu is the Möbius function (A008683).

Mathematica

Table[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[Sum[(i * MoebiusMu[i]^2 + j * MoebiusMu[j]^2 + k * MoebiusMu[k]^2 + l * MoebiusMu[l]^2 + m * MoebiusMu[m]^2 + o * MoebiusMu[o]^2 + p * MoebiusMu[p]^2 + q * MoebiusMu[q]^2 + r * MoebiusMu[r]^2 + (n - i - j - k - l - m - o - p - q - r) * MoebiusMu[n - i - j - k - l - m - o - p - q - r]^2), {i, j, Floor[(n - j - k - l - m - o - p - q - r)/2]}], {j, k, Floor[(n - k - l - m - o - p - q - r)/3]}], {k, l, Floor[(n - l - m - o - p - q - r)/4]}], {l, m, Floor[(n - m - o - p - q - r)/5]}], {m, o, Floor[(n - o - p - q - r)/6]}], {o, p, Floor[(n - p - q - r)/7]}], {p, q, Floor[(n - q - r)/8]}], {q, r, Floor[(n - r)/9]}], {r, Floor[n/10]}], {n, 0, 80}]

Crossrefs

Cf. A008683, A309464, A309478, A309479, A309480, A309481, A309482, A309484, A309485, A309486.

Sequence in context: A214957 A367354 A326627 * A326588 A309357 A051803

Adjacent sequences: A309483 A309484 A309485 * A309487 A309488 A309489

Keyword

nonn

Author

Wesley Ivan Hurt, Aug 04 2019

Status

approved